Trapezoid Area Calculator – Enter the two parallel sides and the height to get the area of a trapezoid instantly — along with the perimeter, median length, leg lengths, and a to-scale diagram you can check at a glance.
Solve for different variables
Area
A = ((a + b) ÷ 2) × h
Use when the two base lengths and the height are known.Height
h = 2A ÷ (a + b)
Use the solve-for-height option when the area is known.Base
b = (2A ÷ h) − a
Rearrange the formula to solve for a missing parallel side.Results
- Height h
- 4 cm
- Median (mid-line)
- 8 cm
- Perimeter
- —
- Left leg c
- —
- Right leg d
- —
- Height as % of base a
- 40%
Area = (a + b) ÷ 2 × h = (10 + 6) ÷ 2 × 4 = 24 cm²
Scale diagram
Drawn to scale from your inputs. The dashed line is the height — the perpendicular distance between the parallel sides, not the slanted leg.
Area growth as the height increases
Each bar uses the same bases with a taller height. Area is directly proportional to height, so the bars rise in a straight line.
Comparison chart
| Scenario | Base a | Base b | Height h | Area |
|---|---|---|---|---|
| Current | 10 | 6 | 4 | 24 |
| Double height | 10 | 6 | 8 | 48 |
| Wider bases | 12 | 8 | 4 | 40 |
| Steeper slope | 14 | 6 | 5 | 50 |
Popular use cases
Roofing
Estimate the area of a roof plane or truss section before ordering shingles or underlayment.
Landscaping
Measure trapezoidal beds, channels, and garden sections for stone, mulch, or topsoil.
Construction
Check cross-sections for ramps, retaining walls, drainage channels, and embankments.
Classroom math
Use it for geometry homework, formula practice, and quick verification of textbook answers.
Examples with images
Basic example
A = ((10 + 6) ÷ 2) × 4 = 32.
Isosceles shape
Both legs are equal, so the shape stays balanced and the leg length can be estimated from the height.
Real-world use
Roofing and civil work rely on trapezoid area because the width often varies across a run.
What the trapezoid really is
A trapezoid is a quadrilateral that has exactly one pair of parallel sides. The bases (usually shown as a and b) are the two parallel sides, while the perpendicular distance between them is the height (h). The other 2 sides are the legs. This calculator will accept bases and height and return the area right away, as well as the perimeter, the median line, and a picture you can draw to scale and then sanity check the number.
There is one vocabulary note: In the U.S. a trapezoid has only one pair of parallel sides; in the UK a trapezoid has at least one pair of parallel sides. The maths is the same, but the label is different.
Area of a trapezoid formula
A = (a + b) ÷ 2 × h is the standard trapezoid formula for the area, with a and b being the parallel sides, and h being the perpendicular height. This is the most standardized version for use in school and field estimates.
How to calculate the height of a trapezoid.
Rearrange the area formula to h = 2A ÷ (a + b). If the base lengths are known and the area is known but the height is not known.
Trapezoid perimeter formula
Perimeter is P = a + b + c + d and c and d are the legs. When the trapezoid is isosceles, the perimeter can be estimated from the bases and height, and the legs are equal.
How the trapezoid area formula works
The formula for area is (a + b) / 2 × h and you should not just memorise it, but understand how it is derived. Construct two congruent trapezoids then rotate one of them 180° around the center of the plane. When they are joined together on their legs, they form a parallelogram with a base (a + b) and a height of h. That is an area of (a + b) × h, but it is formed of two of your trapezoids, and each one of these is half. This is the complete recipe.
Read it again in a different manner. When two bases are given the length of the mid-line or median is the average of the two bases, a + b / 2. Thus, area is equal to the product of the median and height. A trapezoid whose bases are 10 and 6 has the same area as an 8 by 4 rectangle.
The values were pre-filled in the tool: bases 10 cm and 6 cm, height 4 cm. The average base is (10 + 6) ÷ 2 = 8 cm, so the area is 8 × 4 = 32 cm². They increase by a factor of 2 when the height is doubled and a factor of 4 when the bases are doubled.
Perimeter, legs and the remainder of the shape.
In addition to the properties, there is area. The perimeter is a + b + c + d, where c and d are the legs. If you know the legs, enter them in the optional fields and the tool calculates the sum of the legs. If you don’t know them, but the trapezoid is isosceles (the typical school problem and the symmetrical design), this can be found.
In an isosceles trapezoid, let down perpendiculars from each end of the shorter base to the longer base. This cuts out a central rectangle and two congruent right triangles. Each triangle is h by (a − b) ½ and Pythagoras gives the leg as the square root of h² + (a − b) ½², or the square root of (h − ½(a − b))(h + ½(a − b)). It does just this when the isosceles box is checked.
Real-world uses
The most frequent one is roofing. Roofers quote to order shingles, underlayment and flashing, and a hip roof plane is trapezoidal. Next landscaping and civil work: The cost of a trapezoidal drainage channel, a road embankment or a retaining wall cross section is a function of the volume, beginning with the area of the trapezoid times the length. It is also common when an estimate of gravel or topsoil needs to be made for a driveway which widens from a wide street entrance to narrow gate.
The trapezoid is the first shape in the classroom where the students encounter the idea that a formula can be manipulated, not just used to plug numbers into. Solve for the height and you get h = 2A ÷ (a + b); solve for a base and you get b = (2A ÷ h) − a. This tool reads the height case directly if you check the box “I know the area instead”.
Common errors to watch out for
- If the leg is slanted, then use the slanted leg as the height. The height must be at right angles to the bases. Measurements taken along the leg give too large an area.
- Forgetting to halve the base sum. (a + b) × h is the area of the doubled parallelogram, NOT the area of the trapezoid.
- Mixing units. Always change all measurements to a single unit. The area you want will be a nonsensical number, if you enter a base in inches and the height in feet.
- Assuming all four sides are required. The only measurements needed for area are the two bases and the height. Additional sides won’t contribute to the area.
Related Tools
FAQ’s
What is the area of a trapezoid?
This formula is used for calculating the area: Area = (a + b) / 2 × h, where a and b are the parallel sides and h is the perpendicular distance between them. Alternatively, the height of the median time.
If the area is known, how to find the height?
Rearrange to h = 2A ÷ (a + b). Put in the area and the base of this tool and have the “solve for the height” option checked, and this will calculate the height for you.
Is there any difference between trapezoid and trapezium?
In US usage, yes. UK use: They are different; a trapezium has no parallel sides. Always verify the convention your reference is using.
Is there a right angle in a trapezoid?
Yes. It has two right angles if it is a right trapezoid with one leg perpendicular to the bases. The perpendicular leg is also the height.
What is the median of trapezoid?
The line segment connecting the midpoints of the legs is called the median. This had led to an understanding that its length is the average of the bases (a + b) ÷ 2 and, hence, it is possible to write area as median × height.
Does the area of a trapezoid change when it is turned upside down?
No. The area of a shape will not change if it is rotated or reflected. Only the length of the base segments and the perpendicular height are important.
Last updated: September ️15, 2026
Disclaimer – This trapezoid area calculator is provided for general educational and estimating purposes only. Results are rounded and depend entirely on the values you enter. For construction, engineering, purchasing, or safety-critical decisions, confirm measurements on site and have a qualified professional verify the figures before you commit to materials or costs. A Free Tools accepts no liability for losses arising from use of these estimates.